Publication number | US7038429 B2 |

Publication type | Grant |

Application number | US 10/406,477 |

Publication date | May 2, 2006 |

Filing date | Apr 3, 2003 |

Priority date | Nov 2, 2000 |

Fee status | Lapsed |

Also published as | US6590366, US20030201684 |

Publication number | 10406477, 406477, US 7038429 B2, US 7038429B2, US-B2-7038429, US7038429 B2, US7038429B2 |

Inventors | Douglas Roy Browning, Stephanie Novak |

Original Assignee | General Dynamics Advanced Information Systems, Inc. |

Export Citation | BiBTeX, EndNote, RefMan |

Patent Citations (21), Referenced by (5), Classifications (10), Legal Events (8) | |

External Links: USPTO, USPTO Assignment, Espacenet | |

US 7038429 B2

Abstract

Control system for electromechanical arrangements having open-loop instability. The system includes a control unit that processes sensing signals and provides control signals to maintain a movable member, such as a rotor or shaft, in the desired position. The control unit according to the invention includes a unifying plant compensation filter, which isolates the open-loop instability characteristics so that the shaft is treated as a mass having substantially no open-loop structural properties. In magnetic bearings, the open-loop instability is manifested as negative stiffness. The invention isolates the negative stiffness thus providing for better positive stiffness and improved bandwidth. Various filters, summers, and other operators required to carry out the invention are preferably implemented on a programmed processing platform such as a digital signal processor (DSP) or an arrangement of multiple digital signal processors.

Claims(11)

1. A control unit for suspending a movable member, the control unit having an input for receiving a sensing signal and an output for producing an output signal, the control unit comprising:

a unifying plant compensation filter disposed to receive at least the sensing signal from the input for receiving the sensing signal, the unifying plant compensation filter operable to isolate open-loop instability characteristics so that the movable member is treated as a mass having substantially no open-loop structural properties;

a PID controller connected to the unifying plant compensation filter and the output;

a narrowband controller connected to the input for receiving the sensing signal, the narrowband controller removing at least in part noise caused by imbalances and loading of the movable member; and

a summer connected to the PID controller, the narrowband controller, and the output so as to be operable to produce the output signal.

2. The control unit of claim 1 further comprising a resonance controller connected between the input for receiving the sensing signal and the unifying plant compensation filter.

3. The control unit of claim 2 further comprising a tracking notch filter connected to the input for receiving the sensing signal, the tracking notch filter for removing from the sensing signal narrowband noise caused by imbalances and loading of the movable member.

4. The control unit of claim 3 implemented at least in part by a digital signal processor.

5. The control unit of claim 2 further comprising:

a narrowband controller connected to the input for receiving the sensing signal, the narrowband controller removing at least in part noise caused by imbalances and loading of the movable member; and

a summer connected to the PID controller, the narrowband controller, and the output so as to be operable to produce the output signal.

6. The control unit of claim 5 implemented at least in part by a digital signal processor.

7. The control unit of claim 2 implemented at least in part by a digital signal processor.

8. The control unit of **1** further comprising a tracking notch filter connected to the input for receiving the sensing signal, the tracking notch filter for removing from the sensing signal narrowband noise caused by imbalances and loading of the movable member.

9. The control unit of claim 8 implemented at least in part by a digital signal processor.

10. The control unit of claim 1 implemented at least in part by a digital signal processor.

11. The control unit of claim 1 implemented at least in part by a digital signal processor.

Description

This application is a divisional application of, and claims priority from, U.S. patent application Ser. No. 09/704,929, filed Nov. 2, 2000 now U.S. Pat. No. 6,590,366, the entire disclosure of which is incorporated herein by reference.

The U.S. Government has a paid-up license in this invention and the right in limited circumstances to require the patent owner to license others on reasonable terms as provided for by the terms of contract No. N00024-91-C-4355 awarded by the United States Navy.

1. Field of the Invention

This invention is related to the field of electronic control systems. More particularly, this invention is related to a control system of the type based on microprocessors, for controlling electromechanical devices. It is particularly useful as a magnetic bearing control system for a magnetic bearing arrangement, such as the type used to levitate a rotating shaft.

2. Description of the Problem

The problem of lubrication and wear in moving mechanical parts is as old as the utilization of mechanical devices. Various schemes have been devised to eliminate or reduce either or both of these problems with varying degrees of success. One way of alleviating these problems in rotating machines is to use magnetic bearings. Magnetic bearings are well known. A magnetic bearing allows a movable member (a rotor) of a machine to rotate freely with very little friction. This lack of friction is achieved by suspending the movable member, usually a shaft, within a housing lined with magnetic devices, so that the shaft can rotate without touching any solid surfaces. The shaft is suspended or levitated by magnetic fields.

**110**, which runs perpendicular to the paper. A disk, **109**, made of laminated magnetic material is fixed to shaft **110**. Four magnets, **101**, **102**, **103**, and **104**, are attached to a housing and distributed around the disk, **109**. Electrical coils **105**, **106**, **107**, and **108**, are wound around the magnets and control the magnetic fields. In most cases, the magnet/coil combinations work in pairs. For example, magnets **101** and **103** work as a pair to control levitation of the shaft in the up/down direction in the drawing, and magnets **102** and **104** likewise work as a pair to control movement in the left/right direction. The housing for this bearing is not shown so that the details of the bearing itself can be shown more clearly.

**201** is a shaft, which is situated along axis **202**. Laminated disk **205** is acted upon by bearing **204**, which is shown in simplified form for clarity, but in reality includes an arrangement of magnets like that shown in **204** is called an “inboard” radial bearing. Likewise, bearing **203** acts on disk **206**. Again, assuming a driving motor located down axis **202** to the right, magnetic bearing **203** is called an “outboard” radial bearing. Housing **207** contains what is commonly known as a “thrust” bearing, and contains two electrically controlled magnets, **209** and **210**, as well as an appropriate position sensor. These magnets act on disk **208** to control movement and position of the shaft along the axis **202** from left to right. The magnetic bearing system shown in

Generally, sophisticated electronics are required to vary the amount of field produced by the magnets in an electromechanical device such as a magnetic bearing. Control signals are produced for the magnets in response to position signals in order to maintain the rotor in levitation regardless of changing loads and/or mechanical conditions. The present commercial practice for active magnetic bearing control systems is a design in which each axis to be controlled, typically two orthogonal radial directions and one axial (thrust) direction, possesses an independent proportional-integral (PI), proportional-derivative (PD) or proportional-integral-derivative (PID) controller. However, electromechanical devices like magnetic bearings are difficult to control because they are inherently unstable, and so they have found only limited use in industry.

A well-known technique for controlling stable electromechanical systems is to employ the concept of a “unified plant.” As an example, consider the control system of **302**, consists of PID controllers, **303**, and a compensator, **304**. In this approach, a signal from the plant, P, **301**, is passed through a matrix of digital filters in the compensator. The multidimensional filter undoes to some extent the transmission characteristics of the multi-dimensional plant. The filter operates on a vector of error signals measured at point **305**. The filtering allows the controller gains to be increased theoretically without limit for an ideal stable plant with no time delay or other nonlinearity. The extent to which these gains can actually be increased is limited by how well the filter approximates the plant inverse and by any constraints on the power output.

The system above works well with stable plants. However, many practical electromechanical systems exhibit open-loop instability. Magnetic bearings, for example, exhibit a type of open-loop instability called “negative stiffness.” Applying the unified plant approach to such a system is complicated due to the presence of this negative stiffness. To understand what is meant by negative stiffness, assume for the time being the absence of gravity. Allow a shaft to be balanced at its equilibrium position, as shown in **401**, and a magnetic bearing made up of four magnets, a left top (LT) magnet, **402**, a right top (RT) magnet, **403**, a left bottom (LB) magnet, **404**, and a right bottom (RB) magnet, **405**. If the bearing had positive stiffness, perturbations from equilibrium result in a restoring force that pulls the shaft back to equilibrium. The larger the perturbation, the stronger the restoring force. However, negative stiffness implies an unstable equilibrium. If the forces on the magnets are exactly balanced as shown in

Some form of PI, PD or PID control is generally sufficient to overcome negative stiffness so that the shaft can be levitated. However, in order for the shaft to remain suspended under changing loads, the closed loop positive stiffness, and hence the feedback gains must be large. The resistance of the bearing to motion caused by changing loads is referred to as its “dynamics stiffness”. In uncompensated systems, the large feedback gains required for dynamic stiffness cause stability problems related to plant dynamics other than negative stiffness. This will be the case when non-linear dynamic characteristics (e.g., time-delay) and when cross-response structural resonances are present in the sensor bandwidth. Due to the above-described instability problems, current magnetic bearing control systems have major drawbacks. Such systems exhibit stability sensitivity and relatively narrow controller bandwidth in each direction. There are alternative approaches for improving dynamic stiffness that involve deriving an adequate, low-order model from measurements or simulation data. These are referred to as state-space models. This derivation is not straight-forward, and can require significant off-line time by a very skilled practitioner in the control theory and system identification fields. Automated design algorithms are often intractable for complex, highly dynamic, electromechanical systems. Therefore, control systems based on state-space models are difficult to design and expensive to use in commercial applications. What is needed is a new type of control system that can handle open-loop instability such as negative stiffness, but that can also be based on a unified plant so that the control system is more straightforward to adapt to various electromechanical arrangements.

The present invention solves the above problems by providing a stand-alone, wide-bandwidth control system without the drawbacks of inadequate compensation, cross-coupling sensitivity, and lack of resonance control. A high performance multi-dimensional control system is realized with higher feedback gains, without the attendant threat of instability from uncompensated dynamics. For magnetic bearings, the control system of the invention offers high magnetic bearing stiffness over a wide bandwidth. Implementing this new architecture on a real-time processing platform as a stand-alone system can make the control system of the invention attractive for practical commercial implementation. The control system is particularly useful for magnetic bearings but can be adapted to any electromechanical device or arrangement that exhibits open-loop instability.

A magnetic bearing system that makes use of the invention includes one or more magnetic bearings operable to suspend a movable member in response to control signals. In one embodiment, sensors are co-located with the bearings to detect displacement of the movable member. The sensors provide sensing signals. A control unit within the control system for the bearings processes the sensing signals. The control unit according to one embodiment of the invention provides, for each bearing/sensor direction, a control signal or an output signal so that the magnetic bearing maintains the movable member in the desired position. The control unit according to one embodiment of the invention includes a specially designed compensation filter, which isolates the negative stiffness by removing substantially all plant dynamics except the negative stiffness characteristic so that the movable member is treated as a pure mass, thus providing for better stiffness, improved bandwidth, and other improved characteristics. The control unit output signal or signals may be the control signal or signals that are fed to a magnetic bearing, or the control unit output signals may be a portion of the control signals or may need to be amplified or otherwise processed to produce the actual control signals.

The control unit according to one embodiment of the invention has inputs for receiving sensing signals, a set-point signal, and a tachometer signal. The control unit outputs an output signal or a control signal for each axis to be controlled. In one embodiment, the control unit includes a resonance controller for adaptively filtering a negated sensing signal and producing a resonance controller output signal from the filter. A summer is connected to the resonance controller, and adds the set point signal and the negated sensing signal with the resonance controller output signal to produce an error signal. A compensation filter, sometimes called, “a compensator”, is also connected to the first summer for processing the error signal and producing a compensator output signal. The multi-dimensional compensation filter isolates open-loop instability (negative stiffness in the case of magnetic bearings) so that the movable member is treated as a pure mass. The control unit also includes a band-shaping filter. The control unit in one embodiment also includes a proportional-integral-derivative (PID), proportional-integral (PI), or a proportional-derivative (PD) vector to control signals with a PID, Pi, or PD controller, respectively. At some places in this disclosure we use the term “PID vector” or “PID controller” to refer to an element that can be any of these. In many cases, the movable member is a shaft that rotates. The PID controller produces all or a portion of the control unit output signal. A narrowband controller connected to the sensing signal and the tachometer signal input provides a signal that compensates for imbalance forces that occur when the shaft rotates. In this case, another summer adds the PID controller output signal and the narrowband controller output signal to produce the control unit output signal. Instead of a separate narrowband controller to cancel imbalance forces due to shaft rotation, a tracking notch filter is sometimes used to remove those narrowband components from the control signal. The notch filter would typically filter the digitized sensing signal with the frequency of the notch determined by the tachometer signal.

The various filters, summers, and other operators required to carry out the invention are preferably implemented on a programmed processing platform such as a digital signal processor (DSP) or an arrangement of multiple digital signal processors. Such an implementation makes it possible to execute any software or microcode necessary to carry out the high-speed filtering required by the compensator of the invention. The construction of the compensator is typically done off-line, that is by way of background as opposed to real-time processing. Constructing compensators that adjust for changes in the magnetic bearing dynamics requires real-time system identification, as well as processing of the compensation algorithms even though these processes occur at a slower rate than the control processing. The real-time and background processing software or microcode in combination with the processing hardware forms the means to implement the invention. Such a system can be used to implement only the control unit, or it can be used to implement all aspects of the control system.

Control System Overview

**502**, represents the open-loop relationships between control input signals and sensor signals, disregarding the magnetic bearing intrinsic negative stiffness properties shown at **509** as K_{n}. Here, the MIMO plant, **502**, is a five by five matrix linking the five controlled axes to the five sensor pairs used to detect shaft displacement from the desired centered position. The K_{n }block is also a five by five matrix describing the physical negative stiffness relationship between each axis. The current-drive amplifiers, G_{pwm }(five total), **508**, are pulse-width-modulated amplifiers that deliver current to each of the five bearings. Bearing gain K_{f }(five by one vector), **501**, simply depicts the relationship between current flowing in the electromagnet coils and the resultant force applied to the shaft (rotor). Sensor gain G_{sen }(five by one vector), **504**, converts absolute displacement in mils to a voltage signal that the control system can operate on.

Within block **503** labeled DSP's is the proposed compensation and controller architecture, which we call the “control unit”, depicted in block diagram form. Block **506** labeled G_{comp }includes the compensation filter matrix and a control band shaping filter vector. The compensation filter is designed using least-squares methods to unify and orthogonalize the open loop plant. The negative stiffness characteristic is isolated, as further described later, during the compensation filter calculation so that only the stable open loop dynamic elements of the MIMO plant are included in the calculation. This form of compensation makes the compensated system appear as a pure mass (no open-loop structural properties such as resonances) in each of the controlled directions with no cross-coupling between axes. As a result, five independent PID controllers in block **510** can be provided without additional consideration given to high frequency uncompensated dynamics. The compensation filter matrix has already produced the de-coupled compensation over a bandwidth much wider than the desired closed loop bandwidth. A final element in the G_{comp }block is the control band shaping filter (five by one vector). This filter shapes the control band to limit controller response to the desired frequency regions as well as provide robustness to out-of-band sensor noise and high frequency estimation errors associated with the least squares curve fitting algorithms.

The F_{res }block, **505**, contains a five by five matrix of finite impulse response (FIR) filters that also operate directly on the sensor signals. The elements of this matrix are designed according to a known filtering technique designed to suppress resonant dynamics in structures. This filtering technique is described in U.S. Pat. No. 5,816,122, which is incorporated herein by reference. Calculation of the filter coefficients is performed after the inner control loops are closed. Dynamic measurements are then performed to characterize any resonances in the closed-loop response. The remaining block, **507**, within the DSP environs is the narrowband controller, G_{NB}. This five by one vector is a multi-dimensional, adaptive narrowband control signal constructed from the sensor signal and from the tachometer signal, which measures the shaft rotation speed. The narrowband control signals reduce synchronous motion and/or forces induced from rotor imbalances or shaft loading at frequencies associated with rotor speed. Alternatively, tracking notch filters operating directly on the digitized sensor signals can be used to remove from the control signal the synchronous narrowband components caused by imbalances and loading of the shaft, consequently removing synchronous restoring forces from the overall control system.

Additional signals are indicated in _{con }is the output voltage or control signal being produced by the control unit. I_{con }is the current flowing in the magnetic coils of the bearings. F_{con }represents the control forces for the rotating shaft (rotor). In _{ext }is the disturbance signal component of the measured displacement caused by external forces acting on a suspended rotor. d_{int }is an internal disturbance signal that enters through the same path as the control signal. V_{sen }is the output voltage from the magnetic bearing sensors, V_{set }is a set point voltage that corresponds to the desired position of the rotor, and V_{err }is an error voltage signal that is derived by taking the difference between the desired and measured position voltages and adding it to the output of the resonance controller. “tach” refers to a tachometer speed reference signal.

**503** of **601** represented as having entries f_{aa }was omitted from **602** having entries represented by f_{recon }was omitted from **604**, is shown in more detail in

Understanding and Measuring the Plant

In the traditional unifying plant approach, the plant is obtained as follows. A probe signal (band limited white noise filtered by a shaping filter) is applied to the plant and the resulting effect on the error signal is measured. The correlation between the applied probe signal and the error signal determines the transfer function P between each actuator-sensor pair. P is referred to as the plant. Typically the transfer function is expressed in the frequency domain and its amplitude and phase determine the transmission characteristics of the medium. Applying a probe signal in each of the NA actuation directions and measuring the effect at each of the NE errors results in an NAŚNE matrix P(ω) of transfer functions. ω is the frequency in radians per second. The process of unifying the plant for a MIMO system involves taking the matrix inverse of P(ω) at each frequency picket ω and fitting each resulting matrix element with an infinite impulse response (IIR) filter which is the best fit to the inverse transfer function in the least squares sense. The fit is obtained by coming as close as possible to satisfying:

Σ_{ω} *|P* ^{−1}(ω)−*G*(ω)|^{2}≅0.

G(ω) is expressed as a ratio of polynomials in z^{−1 }by:

where z^{−1 }represent a one-sample delay. z^{−1 }is given in terms of ω and the sample rate SR by z^{−1}=e^{−iω/SR}. Fitting the filter involves finding the coefficients b_{i }and a_{i }that minimize the least squares equation for each pair of actuators and errors. Implementing the digital filter in the form shown above as a ratio of tapped delays results in very noisy high order filters. A better approach, once b_{i }and a_{i }have been determined, is to use these coefficients to determine the poles and residues of G. Complex conjugate pairs are then combined to form biquads (or second order sections) with real coefficients. Likewise, the remaining real poles are combined by pairs into biquads, resulting in a filter having sections similar to that shown in

The c and d coefficients have as a dimension the number of actuators (NA) times number of errors (NE) times the number of second order sections (nsect), or NAŚNEŚnsect. The summation is done over the number of biquad sections. The number of sections nsect is one more than the filter order divided by two. Each biquad is order two; the additional section corresponds to the constant term in the definition of the filter. As defined above, G is a matrix of NAŚNE filters.

Negative stiffness has previously been discussed. A mathematical description of positive and negative stiffness comes from the equation of the harmonic oscillator (or spring-mass system), which states that the acceleration {umlaut over (x)} is proportional to the displacement x in such a system, with k the stiffness and m the mass:

*m{umlaut over (x)}=−kx*

The solutions to the above equation are x=Ae^{iωt}+Be^{−iωt }with A and B determined by initial conditions and with the frequency of oscillation in radians per second given by:

If the stiffness k is negative then the two oscillatory solutions become a decaying solution and a growing solution: x=Ae^{−αt}+Be^{αt }with α=−iω. A growing solution means that the dynamics are unstable.

Due to the negative stiffness, it is not possible to directly measure the plant. The plant must be inferred by measuring the closed loop transfer function with the PID controller operating and then extracting with offline processing the unstable plant, which has a well-defined frequency representation despite being unstable. The procedure is to apply just enough control gain to levitate the shaft. This involves either trial and error or some a priori knowledge of the negative stiffness from known properties of the magnets. Then a probe is turned on sequentially for each of the five actuation directions, and data is collected at the five error sensors and at the five outputs of the PID controllers. The transfer function data for the outputs of the PID controllers is in some sense redundant. Knowledge of the PID parameters alone is sufficient to determine this transfer function without measuring it.

**801**, having a transfer function P, and PID controller **803** within a control system **802**. The PID controller has the transfer function C. **805** for measuring the error signal, e, point **806** for measuring the controller output signal, c, point **807** for including a disturbance signal, d, and point **808** for applying the probe and measuring the signal p. The vector equation relating the error signal to the probe and disturbance signals is:

*e=PC*(*p+e*)+*Pd.*

The equation for the control output is given by:

*c=C*(*p+e*).

e, p and c are Fourier transforms of vector error, probe and control time series, respectively. The transfer function from the probe to the errors is:

* is a complex conjugate, < > indicates averaging over several sets of Fourier-transformed data and I is the identity matrix. The disturbance d is uncorrelated with the probe. This matrix equation represents the closed loop transfer function that is measured between each probe and each error signal when the controller is turned on. The closed loop transfer function through the controller is:

The final result in the above equation uses the fact that PC and [I−PC]^{−1 }commute. The open loop plant is given in terms of X and Y by:

XY^{−1}=P.

X and Y are direct measurements of closed loop transfer functions computed from control, probe and error time series. The above relationship between X and Y transfer functions can be observed from the fact that for e in

An alternative way of determining P is to compute the open loop controller transfer function C from known PID gains. In this case the only required measurements are probe and error time series. From the definition of X above:

*P=X[I+X]* ^{−1} *C* ^{−1}.

The first method is preferred because it is closer to a direct measurement, that is, X and Y are both measured whereas C must be calculated theoretically.

Isolating the Negative Stiffness

In order to construct a unifying compensator for the plant P, it is necessary to identify the negative stiffness and isolate it. The most straightforward way of doing this is to fit the plant directly with an IIR filter and find the unstable poles. Alternatively, a condition of minimum phase can be imposed on the inverse plant. Assuming the direct fit method is used, after an examination of the unstable poles, it is found that the plant can be cleanly separated into a product of a fully-coupled stable part and a diagonal unstable part:

P={circumflex over (P)}D

with the matrix elements D_{ij }given by:

δ_{ij }is the Kronecker delta: 1 if i=j and 0 otherwise. The above denominator is a product of two poles β and β^{−1}, which are related to the α of the growing and decaying solutions defined by β=e^{α/SR }where SR is sample rate. Only one of the poles (the growing one) is unstable. Both poles are removed so that D can be made to resemble a spring-mass system. The above numerator is just a normalization designed so that at DC (ω=0 & z=1), D_{ii}=1.0.

Although the above decomposition of P may appear no more than a mathematical construct, it is in fact a physically meaningful decomposition. The negative stiffness poles in P are removed by multiplying each column of P by the reciprocal of D_{ii }above. Although the matrix elements between different directions on the same bearing are essentially zero (eg. P_{21}), the matrix elements between the same direction on two different radial bearings (P_{31}) have their unstable poles at approximately the same location as matrix elements between a collocated actuator and sensor (P_{11}). The new plant, {circumflex over (P)}, that remains after removing the negative stiffness is either stable or occasionally has higher-order unstable poles that are likely artifacts of the fitting process.

In the matrix D above, only one pair of poles β_{i }is identified for each of the five directions. In fact, based on the rigid body model, there can be two unstable poles per direction corresponding to two rigid body modes. In that case, the denominator in D would be a product of the two pairs of poles. Experimental filter fits of P have only identified one pair of poles, which can be assumed to be the dominant contribution to D. In addition, it is usually the case that not all of the poles in the five directions are unique. The stiffness is a property of the magnet and is approximately the same in each bearing direction. Given the above discussion of the spring mass system, the location of the poles is determined by the stiffness and by the mass supported by the bearing axis. For the bearing configuration shown in

**1105**, controller output signal c measured at point **1106**, and probe signal p measured at point **1108** are shown as before. Filter **1104**, with transfer function G, is designed such that G{circumflex over (P)}≅I. Filter **1104** is disposed within control system **1102** as before. The spring-mass system is described as a second order differential equation. The transfer function between an applied force and the displacement involves two integrations, which can be expressed in the z-domain as [1/(1−z^{−1})]^{2}, as shown at **1109**. The negative feedback is described by K/M (or KM^{−1}), which is diagonal but can be different in each of the five directions. The transfer function from the disturbance input, **1107**, to the input at the new plant **1101** ({circumflex over (P)}) can be shown to be D when one makes the identification:

and uses the fact that 1+ln β≅β and 1−ln β≅1/β. In the above k, m and SR are, respectively, stiffness, mass and sample rate. Then [(1−z^{−1})^{2}−(ln β)^{2}] can be factored into (β−z^{−1})(β^{−1}−z^{−1}). (ln β)^{2 }is KM^{−1 }multiplied by a gain of 1/SR^{2 }as shown. These are very good approximations at the high sample rates typically used for magnetic bearings (˜10K).

The PID control signal transfer function may be expressed in the z domain as a diagonal matrix:

*C* _{ij}[λ_{Pi}+λ_{Di}(1*−z* ^{−1})+λ_{Ii}/(1−*z* ^{−1})]δ_{ij}

where λ_{P}, λ_{D }and λ_{I }are respectively the proportional, derivative and integral gains. The proportional gain will have the effect of shifting the poles in D inside the unit circle provided that the applied gain is sufficient to overcome the negative stiffness. Assuming G={circumflex over (P)}^{−1 }and assuming that λ_{D }and λ_{I }are both zero, the denominator of the closed loop transfer function becomes:

1−*gλ* _{Pi} *D* _{norm}−(β_{i}+β_{i} ^{−1})*z* ^{−1} *+z* ^{−2}

with D_{norm}, the normalization, given by D_{norm}=2−(β_{i}+β_{i} ^{−1}). The unstable pole β_{i }of z (not z^{−1}) is shifted according to:

which is within the unit circle provided that the above quantity is less than one. This true whenever:

gλ_{Pi}>1

Although many of the calculations, like the one above, are simpler in the s-domain, the filters are implemented in the z-domain and so an understanding of the processing in the z domain is useful in understanding the invention. The gain g within control system **1102** is chosen such that g approximately equals the diagonal values of {circumflex over (P)} at ω=0. That is, the original DC offset of the plant is put back in order to keep the PID parameter settings in the same range with compensation as without.

_{Pi }is about 0.3. In fact, the input parameter for the proportional gain was chosen to approximately scale with the resonant frequency so:

√{square root over (λ_{Pi})}

was used. It was found that the minimum value of this parameter required to levitate the shaft was about 0.6, which is about equal to:

1*/√{square root over (g)}* for *g=*3.

Unfortunately, g cannot be measured until the shaft is levitated, so the initial estimate for g must be based upon some a priori knowledge of the negative stiffness (g is roughly the reciprocal of the stiffness) or determined by trial and error.

The Compensator

Immediately above we defined G to be the filter fit to the inverse of the plant {circumflex over (P)}, which was the open loop plant P with the negative stiffness piece D removed. For the case of a two-radial bearing system, coupling between orthogonal directions was small, as shown in

Two compensators that can be used to implement the invention have been tested: a quasidiagonal and a diagonal one.

Resonance Controller

The resonance controller used with the invention uses a technique described in U.S. Pat. No. 5,816,122, which is assigned to the assignee of the present invention, and which is incorporated herein by reference. In this resonance control technique, a recursive adaptive filter is applied within an additional feedback path around the compensation and PID control loop. As shown in

The resonance controller matrix F_{res }is nominally a diagonal structure if the compensation filters produce a reasonably orthogonalized closed loop plant. If the closed loop plant remains highly coupled due to poor orthogonalization in the resonance frequency regions, F_{res }may take a non-diagonal form, thereby increasing the computational load caused by the additional filters in F_{res}. For the case where F_{res }can be considered diagonal, each resonance control filter will be associated with a unique magnetic bearing control direction. For example, one bearing in the left-top (LT) to right-bottom (RB) direction would be controlled by the F_{11 }filter in the F_{res }matrix (see _{22 }filter would be associated with the RT to LB direction. Each resonance control filter is implemented as a finite-impulse-response (FIR) filter. The length (number of taps) in each filter is determined from the DSP sampling rate and the frequency of the lowest resonance to be controlled. The coefficients associated with each filter tap are computed adaptively according a filtered-x least mean square (FXLMS) adaptive filter algorithm. This calculation is performed after the necessary closed loop transfer functions are measured with just the compensation filters and PID controller operating. Once the resonance control filters are available, they can be activated as an outer loop controller providing attenuation of the desired modes in the levitated magnetic bearing system.

Narrowband Controller

For the magnetic bearing system described, several well-known techniques for synchronous vibration suppression can be incorporated to reduce vibrational energy associated with synchronous load disturbances and shaft imbalances. _{NB }is nominally a diagonal matrix of narrow band control signals. Typical forms for the narrow band controller shown in _{NB }matrix of

Hardware Implementation

A basic control system can work adequately for some applications without resonance or narrowband controllers. For clarity, such a system is illustrated in the block diagram in

**1** and B**2** in **1901** and four proximity probe sensors, **1902**. The error signals shown in **1801** through computing the difference between opposing proximity probe sensors. This process converts the eight proximity probe inputs into four error signals. Note that in

Signals in **1802** provides the four-by-four matrix of filters, which implement the compensator according to the invention. The negative stiffness is removed from the compensation filter by offline processing as previously described. The compensation block, **1802**, is implemented by the application DSP. After applying a gain, g, each resultant signal is fed to a PID controller which is implemented by the application DSP. Controllers **1803** and **1804** are for bearing B**1** and controllers **1805** and **1806** are for bearing B**2**. Gain g adjusts the root-mean-square (RMS) level of the plant to what it was before the compensator was included so that the PID gains stay at approximately the same values. The control system produces eight output control signals, one for each actuator. Only four of these signals are independent; opposing actuators, as shown in

Probe signals are shown in **1815** is included to shut off bearing B**1**, and on/off switch **1816** shuts of bearing B**2**. Switch **1817** serves as a master switch to shut off the entire control system. These switches can be mechanical or electronic. Also note that the control signal has a threshold applied after each PID controller to avoid damaging the bearing actuators.

Each filter within the compensator is a sum of second order sections. The number of second order sections required for a compensator with this hardware implementation is 4Ś4Śnsect, where nsect is the number of sections in a single filter (for this example, nine) and four-by-four is the number of filters required from four error inputs to four control outputs. **2006** represents an array of 4Ś4Śnsect second order sections (SOS's). The summations on the output signals represent both the sum over sections to obtain the action of one filter on one error time series and the matrix multiplication of a row of filters by a column of error sensor time series. The summation is over 4Śnsect terms. The output of each summation is a single time series. The control system is designed so that the compensator is downloaded initially as an identity matrix. Using an identity compensator, the rotor is levitated and a system identification is computed. A unifying compensator is constructed based on the system identification. The desired unifying compensators are then read in as dSPACE parameter files. The use of parameter files allows the compensator to be changed without recompiling.

**2101**, **2102**, and **2103**. The gain elements **2104** and **2105** are used to scale the input parameters. The parameter values shown in

Testing

Testing showed considerable improvement in PID gains over that of prior-art control systems. In particular, the proportional gain increased by a factor of four. Before describing the improvement in the other gains, it is useful to describe the scaling used for the input parameters. Previously we labeled the PID gains as (λ_{P}, λ_{I}, λ_{D}). In the test DSP implementation the set of input parameters were ({tilde over (λ)}_{P}, {tilde over (λ)}_{I}, {tilde over (λ)}_{D}), where:

The above scaling is designed so that the tilde parameters are dimensionless and, in particular, are independent of sampling rate SR. C is a physical constant that has the dimensions of HZ^{2 }per volt. It can be expressed as C=C′/M where C′ is the conversion of voltages to #/in and M is in slugs #/g where g is acceleration due to gravity. All of the control voltages are multiplied by C. Integrating twice to obtain a displacement from the control forces results in an additional factor of 1/SR^{2}. This scaling has a straightforward physical interpretation. If the negative stiffness were zero (or small compared to the proportional gain) and the open loop transfer function {circumflex over (P)} is the same as that of a wire, then the displacement would have an oscillation frequency ω_{0}=√{square root over (Cλ_{P})}. Defining {tilde over (ω)}_{0}=ω_{0}/SR, the PID gains scale according to

The frequency is factored out of the derivative gain in order for its effective damping to be independent of frequency. The definition of the integral gain in terms of {tilde over (ω)}_{0 }is consistent with the proportional and derivative gains. Each integral results in a factor of {tilde over (ω)}_{0}. The integral gain is also proportional to the scaled derivative gain in order to help maintain stability. In addition to providing infinite DC stiffness, the integral gain opposes the effect of the damping due to derivative gain. If the derivative gain is decreased the integral gain should be decreased proportionally to maintain the same effective damping. With compensation, the scaled derivative gain can be increased by a factor of three and the unscaled gain by a factor of six. The scaled integral gain was unchanged and the unscaled integral gain increased by a factor of 24.

_{P}=0.8, {tilde over (λ)}_{I}=0.0017, {tilde over (λ)}_{D}=0.3] nor compensated [{tilde over (λ)}_{P}=1.7, {tilde over (λ)}_{I}=0.0017, {tilde over (λ)}_{D}=0.9] normalized PID gains are at their maximum levels. These levels are comfortably stable, rather than borderline stable in both cases. The approximate stability limits on the proportional gain are about 1.0 uncompensated and 1.9 compensated for the particular compensator used in

We have described specific embodiments of our invention, which provides an improved control system for electromechanical devices. One of ordinary skill in the magnetic, control and electronics arts will quickly recognize that the invention has numerous other embodiments. In fact, many implementations are possible. The following claims are in no way intended to limit the scope of the invention to the specific embodiments described.

Patent Citations

Cited Patent | Filing date | Publication date | Applicant | Title |
---|---|---|---|---|

US5130589 | Mar 12, 1991 | Jul 14, 1992 | Ebara Corporation | Imbalance correcting apparatus for a rotor |

US5216308 | Jan 27, 1992 | Jun 1, 1993 | Avcon-Advanced Controls Technology, Inc. | Magnetic bearing structure providing radial, axial and moment load bearing support for a rotatable shaft |

US5256952 * | May 29, 1992 | Oct 26, 1993 | Hitachi, Ltd. | Magnetic bearing control method and apparatus |

US5306975 | May 4, 1991 | Apr 26, 1994 | Ant Nachrichtentechnik Gmbh | Vibration insulation of a body on magnetic bearings |

US5347190 | Aug 3, 1990 | Sep 13, 1994 | University Of Virginia Patent Foundation | Magnetic bearing systems |

US5355042 | Nov 13, 1990 | Oct 11, 1994 | University Of Virginia Patent Foundation | Magnetic bearings for pumps, compressors and other rotating machinery |

US5486729 * | Mar 5, 1993 | Jan 23, 1996 | Hitachi, Ltd. | Method and apparatus for controlling a magnetic bearing |

US5543673 | Jul 27, 1993 | Aug 6, 1996 | Sundstrand Corporation | High performance magnetic bearing |

US5572079 | Dec 21, 1994 | Nov 5, 1996 | Magnetic Bearing Technologies, Inc. | Magnetic bearing utilizing brushless generator |

US5720010 * | Aug 19, 1996 | Feb 17, 1998 | Ebara Corporation | Control system for a linear actuator including magnetic bearings for levitating a robot arm |

US5736800 | Oct 18, 1994 | Apr 7, 1998 | Iannello; Victor | Light weight, high performance radial actuator for magnetic bearing systems |

US5816122 | Apr 30, 1996 | Oct 6, 1998 | General Dynamics Advanced Technology Systems, Inc. | Apparatus and method for adaptive suppression of vibrations in mechanical systems |

US5923559 * | Aug 30, 1996 | Jul 13, 1999 | Seiko Seiki Kabushiki Kaisha | Magnetic bearing apparatus |

US5925957 | May 30, 1997 | Jul 20, 1999 | Electric Boat Corporation | Fault-tolerant magnetic bearing control system architecture |

US5986373 | Jan 13, 1998 | Nov 16, 1999 | Stucker; Leland | Magnetic bearing assembly |

US5998899 * | Jun 12, 1997 | Dec 7, 1999 | Rosen Motors L.P. | Magnetic bearing system including a control system for a flywheel and method for operating same |

US6005315 * | Jun 3, 1998 | Dec 21, 1999 | Electric Boat Corporation | Fault-tolerant magnetic bearing control system architecture |

US6107770 * | Jan 26, 1999 | Aug 22, 2000 | Lockheed Martin Corporation | Control system for counter-oscillating masses |

US6208051 * | Mar 17, 1995 | Mar 27, 2001 | Seiko Seiki Kabushiki Kaisha | Spindle apparatus |

US6267876 * | Jul 28, 1999 | Jul 31, 2001 | Trinity Flywheel Power | Control of magnetic bearing-supported rotors |

US6589030 * | Jun 19, 2001 | Jul 8, 2003 | Ntn Corporation | Magnetically levitated pump apparatus |

Referenced by

Citing Patent | Filing date | Publication date | Applicant | Title |
---|---|---|---|---|

US8853905 * | Dec 27, 2012 | Oct 7, 2014 | Osaka Vacuum, Ltd. | Radial direction controller and magnetic bearing apparatus utilizing same |

US9388854 * | Dec 9, 2013 | Jul 12, 2016 | Ebara Corporation | Magnetic bearing apparatus and method for reducing vibration caused by magnetic bearing apparatus |

US20140159526 * | Dec 27, 2012 | Jun 12, 2014 | Osaka Vacuum Ltd. | Radial direction controller and magnetic bearing apparatus utilizing same |

US20140175925 * | Dec 9, 2013 | Jun 26, 2014 | Ebara Corporation | Magnetic bearing apparatus and method for reducing vibration caused by magnetic bearing apparatus |

US20160164396 * | Aug 11, 2014 | Jun 9, 2016 | Zentrum Mikroelektronik Dresden Ag | Adaptive controller based on transient normalization |

Classifications

U.S. Classification | 322/49, 310/90.5, 310/90 |

International Classification | H02P9/40, H02K5/16, H02K7/08, F16C39/06, H02K7/09 |

Cooperative Classification | F16C32/0451 |

European Classification | F16C32/04M4C4 |

Legal Events

Date | Code | Event | Description |
---|---|---|---|

Jul 25, 2003 | AS | Assignment | Owner name: GENERAL DYNAMICS GOVERNMENT SYSTEMS CORPORATION, V Free format text: MERGER;ASSIGNOR:GENERAL DYNAMICS ADVANCED TECHNOLOGY SYSTEMS, INC.;REEL/FRAME:014313/0064 Effective date: 20021219 |

Aug 18, 2003 | AS | Assignment | Owner name: GENERAL DYNAMICS ADVANCED INFORMATION SYSTEMS, INC Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:GENERAL DYNAMICS GOVERNMENT SYSTEMS CORPORATION;REEL/FRAME:013879/0250 Effective date: 20030718 |

Dec 7, 2009 | REMI | Maintenance fee reminder mailed | |

May 3, 2010 | SULP | Surcharge for late payment | |

May 3, 2010 | FPAY | Fee payment | Year of fee payment: 4 |

Dec 13, 2013 | REMI | Maintenance fee reminder mailed | |

May 2, 2014 | LAPS | Lapse for failure to pay maintenance fees | |

Jun 24, 2014 | FP | Expired due to failure to pay maintenance fee | Effective date: 20140502 |

Rotate